Split the chicken breasts in half to make 4 thin breasts, then cut into 2-inch pieces.
Set up your dredging station: In a shallow bowl, combine the flour, 1 tablespoon salt, onion powder, garlic powder, cayenne and 1/2 teaspoon black pepper. In another shallow bowl, crack in the eggs and add in the remaining teaspoon of salt and 1/2 teaspoon black pepper. Mix together to break the yolks.
Heat a 10 or 12 inch skillet over medium heat and pour in a 1/4 inch of oil to coat the bottom of the pan. Once hot, start working in batches of about a dozen nuggets: For each piece of chicken, dredge it in the flour to coat, then dip in the egg to cover completely, and dredge again in the flour mixture. Then add to the pan. Repeat leaving 1/2-inch between each chicken nugget.
Fry the nuggets for 6-8 minutes per side until golden brown on the bottom, then flip and finish cooking on the other side. Remove them to a sheet pan fitted with a cooling rack to drain. If you're planning to eat all nuggets, consider putting the pan in a warm oven (about 200 F) to keep them warm between batches. Repeat process with all chicken, until all your nuggets are cooked. Serve with dipping sauces or let cool completely and freeze.